APPROXIMATION OF CONTINUOUS-TIME STOCHASTIC-PROCESSES BY A LOCAL LINEARIZATION METHOD

This paper investigates the rate of convergence of an alternative appr oximation method for stochastic differential equations. The rates of c onvergence of the one-step and multi-step approximation errors are pro ved to be O((Delta t)(2)) and O(Delta t) in the L-p sense respectively , where Delta t is discrete time interval. The rate of convergence of the one-step approximation error is improved as compared with methods assuming the value of Brownian motion to be known only at discrete tim e. Through numerical experiments, the rate of convergence of the multi -step approximation error is seen to be much faster than in the conven tional method.